Institut de Mathématiques de Toulouse

Les événements de la journée


3 events


  • MathOcéan

    Monday 17 June 14:00-15:00 - Roberta Bianchini - ENS Lyon

    Reflection of internal waves from a sloping boundary

    Résumé : Internal waves describe the (linear) response of an incompressible stably stratified fluid to small perturbations. The angle between the group velocity and the vertical is completely determined by their frequency. Therefore the reflection on a sloping boundary is expected to be singular if the slope has the same inclination as the group velocity. In this talk, we explore this critical geometry for the the weakly viscous and weakly nonlinear Boussinesq equations.

    Lieu : Bâtiment 1R3, salle MIP

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  • Séminaire doctorants Picard

    Monday 17 June 14:00-15:00 - Benoît Cadorel

    C’est quoi… l’hyperbolicité complexe ?

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  • MathOcéan

    Monday 17 June 15:00-16:00 - Tomas Lundquist - Université Paul Sabatier

    Energy methods in continuous and discrete time

    Résumé : For the design and analysis of stable boundary procedures of hyperbolic problems, some of the most widely successful and generally applicable strategies involve the use of energy methods. By adopting a discrete formalism centered on achieving key properties such as integration-by-parts, energy proofs of well-posedness can be mimicked more or less exactly in order to prove stability of a numerical scheme. For this to be possible, the discrete operations of integration and differentiation must be tightly coupled, and often special care must be taken when imposing physical or artificial boundary conditions. In recent years, operators with a formal summation-by-parts property have been used with great success to fashion provably stable discretizations on complex geometries involving e.g. numerical boundary conditions, multi-block or hybrid interface couplings, curvilinear transformations and moving meshes. This emerging summation-by-parts framework has so far been exclusively focused on method-of-lines type techniques, where it can be applied to a wide range of numerical methods including finite element, finite difference and finite volume methods. In this talk we review some of the latest developments in energy stable numerical techniques, including generalized definitions of summation-by-parts operators, weak boundary/interface conditions and numerical filters. We will also discuss challenges and possible benefits from extending the summation-by-parts idea to discrete time, with particular focus on schemes of Lax-Friedrichs or Lax-Wendroff type.

    Lieu : Bâtiment 1R3, salle MIP

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